Estimating optical transmission system penalties induced by polarization mode dispersion (PMD)

ABSTRACT

Polarization mode dispersion (PMD) induced system penalty ε is determined from optical characteristics of an optical wavelength division multiplexed (WDM) signal that is carried on a network. The method involves tapping the optical WDM signal, separating an optical channel from the tapped optical WDM signal, performing a frequency-resolved state of polarization (SOP) measurement on the channel, and computing the PMD-induced system penalty as ε=AL 2 +BL 4 , in which A and B are predetermined parameters and L is an SOP string length based on the SOP measurement.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority to U.S. provisional application60/699,107, filed Jul. 14, 2005, which is incorporated herein byreference in its entirety.

This application may be considered to be related to co-pending U.S.application Ser. No. 10/825,529, filed Apr. 15, 2004 now U.S. Pat. No.7,174,107, entitled Method and Apparatus for MeasuringFrequency-Resolved States of Polarization of a Working Optical ChannelUsing Polarization-Scrambled Heterodyning and having common inventorshipand ownership with the present patent application. This patentapplication is incorporated herein by reference.

BACKGROUND

1. Field of the Invention

This invention relates to arrangements for measuring polarization modedispersion (PMD) in optical communication fibers. More specifically, theinvention relates to arrangements for determining which portion of fibercommunication system penalty is induced by first-order and all-orderPMD.

2. Background Art

Optical fiber communications systems are subject to system penaltiesthat derive from a variety of sources, only one of which is polarizationmode dispersion (PMD). Other sources that can degrade system performanceinclude, for example, chromatic dispersion, multi-path interference andnonlinear effects.

When a fiber's performance has been inadequate or failing, conventionalsystems have not been able to readily isolate the causes of anyperformance degradation, or measure the relative contributions of thedegradation sources. It has sometimes been necessary to bring a systemoffline in order to perform experiments that can isolate the cause of aproblem. This inability to readily diagnose the problem source(s) hasthwarted predictions of system performance and prevented efficient andfocused attempts to correct performance problems.

Thus, there is a need in the art to readily monitor and evaluatePMD-induced effects in optical transmission systems, to allow systemoutages to be predicted, corrected or prevented.

REFERENCES

-   Ref. 1. M. Shtaif, M. Boroditsky, “The effect of the frequency    dependence of PMD on the performance of optical communications    systems”, Photon. Technol. Lett., 15(10) pp. 1369-1371, 2003.-   Ref. 2. P. J. Winzer, H. Kogelnik, C. H. Kim, H. Kim, R. M.    Jopson, L. E. Nelson, and K. Ramanan, “Receiver impact on    first-order PMD outage,” Photon. Technol. Lett., 15, pp. 1482-4,    2003.-   Ref. 3. H. Kogelnik, R. M. Jopson, L. E. Nelson, “Polarization Mode    Dispersion,” in Optical Fiber Communications, I. Kaminow, Ed, Vol.    IVb, San Diego, Academic Press, (2002), pp. 745-762.-   Ref. 4. Boroditsky et al., “Viewing polarization ‘strings’ on    working channels: High-resolution heterodyne polarimetry,” Proc ECOC    2004, Paper We5.4.5.-   Ref. 5. L. E. Nelson, R. M. Jopson, H. Kogelnik, G. J. Foschini,    “Measurement of depolarization and scaling associated with    second-order polarization mode dispersion in optical fibers,” IEEE    Photon. Technology Letters, 11 (12) pp. 1614-1616, 1999.-   Ref. 6. P. Westbrook et al., “Wavelength sensitive polarimeter for    multichannel polarization and PMD monitoring,” in Proc. OFC 2002,    paper WK5.-   Ref. 7. S. X. Wang, A. M. Weiner “Fast wavelength-parallel    polarimeter for broadband optical networks,” Optics Lett., 29, pp    932-925, 2004.-   Ref. 8. C. Antonelli et al., “PMD-induced penalty statistics fiber    links,” IEEE Photon. Technology Letters, 17(5), pp 1013-1015, May    2005.

All references, including patents and patent applications, cited in thisspecification are incorporated herein by reference.

SUMMARY

A method determines polarization mode dispersion (PMD) induced systempenalty ε from optical characteristics of an optical wavelength divisionmultiplexed (WDM) signal carried on a network. The method involvestapping the optical WDM signal, separating an optical channel from thetapped optical WDM signal, performing a frequency-resolved state ofpolarization (SOP) measurement on the channel, and computing thePMD-induced system penalty as ε=AL²+BL⁴, in which A and B arepredetermined parameters and L is an SOP string length based on the SOPmeasurement.

BRIEF DESCRIPTION OF THE DRAWINGS

A more complete appreciation of the described embodiments is betterunderstood by reference to the following Detailed Description consideredin connection with the accompanying drawings, in which like referencenumerals refer to identical or corresponding parts throughout, and inwhich:

FIG. 1 shows an experimental setup to measure the opticalsignal-to-noise ratio (OSNR), bit error rate (BER), state ofpolarization (SOP) and polarization mode dispersion (PMD) in rapidsequence;

FIG. 2 shows first order PMD data for differential group delays (DGDs)of 26 ps (circles) and 60 ps (squares), with respective quadratic andquartic fits, the inset showing an optical eye for a back-to-backmeasurement;

FIG. 3 illustrates all-order PMD data, with a lower bound provided by aquartic approximation for the first order data of FIG. 2;

FIG. 4 shows mean penalty value vs. SOP string length for first orderand all-order PMD fibers, the range of penalty values being shown byerror bars and the inset comparing the SOP drift for the three PMDs;

FIG. 5 shows penalty spread vs. magnitude of the second order PMDvector; and

FIG. 6 is a flowchart of one practical embodiment of a method ofdetermining the polarization mode dispersion (PMD) induced systempenalty ε of an optical transmission system.

DETAILED DESCRIPTION

In describing embodiments illustrated in the drawings, specificterminology is employed for the sake of clarity. However, the inventionis not intended to be limited to the specific terminology so selected,and it is to be understood that each specific element includes alltechnical equivalents that operate in a similar manner to accomplish asimilar purpose. Various terms that are used in this specification areto be given their broadest reasonable interpretation when used tointerpret the claims.

Moreover, features and procedures whose implementations are well knownto those skilled in the art are omitted for brevity. For example,initiation and termination of loops, and the corresponding incrementingand testing of loop variables, may be only briefly mentioned orillustrated, their details being easily surmised by skilled artisans.Thus, the steps involved in methods described herein may be readilyimplemented by those skilled in the art without undue experimentation.

Further, various aspects, features and embodiments may be described as aprocess that can be depicted as a flowchart, a flow diagram, a structurediagram, or a block diagram. Although a flowchart may describe theoperations as a sequential process, many of the operations can beperformed in parallel, concurrently, or in a different order than thatdescribed. Operations not needed or desired for a particularimplementation may be omitted. A process or steps thereof may correspondto a method, a function, a procedure, a subroutine, a subprogram, and soforth, or any combination thereof.

The invention provides arrangements to measure system degradation thatis induced by polarization mode dispersion (PMD), and to separate itfrom other impairment sources. That is, the invention permits one todetermine if errors in a network are due to PMD or some other fault suchas fiber loss, failing amplifiers, and so on.

One method involves spectrally separating a portion of the signal ofinterest, measuring frequency-resolved state of polarization of saidmodulated signal, and calculating the system penalty (such aseye-closure penalty or OSNR penalty) from the measurement. Themeasurement result can be used either as a channel quality estimate oras a feedback signal for channel PMD mitigation.

Both experimentally and numerically, a correlation has been establishedbetween PMD-induced system degradation, characterized by eye penalty orOSNR penalty, and the measurable frequency resolved output state ofpolarization of the operation optical channel. One embodiment of amethod operates “in-service”, that is without need to interrupt theservice.

The method uses a novel signal characteristic that is correlated withsystem performance against a random, time-varying impairment.Experiments have measured the PMD-induced system penalty arising fromfirst-order and all-order PMD. A measurable quantity, herein referred toas “string” length, parameterizes the penalty. It finds a deterministiccorrection to the accepted first-order PMD-induced system penaltyapproximation. Higher orders of PMD are shown to introduce an additionalpenalty scatter that is nearly independent of “string” length, andcorrelated to the magnitude of the second order PMD vector.

Polarization-mode dispersion has the potential to become a significantlimiting factor in high speed optical communication systems. Thus, adetailed understanding of PMD statistics, dynamics, and resulting systemimpairments are important for successful implementation of mitigationtechniques (see, for example, references 1, 2). Since a system's PMDtolerance is related to many parameters, including the modulation formatand receiver design, PMD-induced system impairments are oftenapproximated. Commonly, only the first order effect of PMD isconsidered. The present arrangement measures PMD-induced system penaltyfrom not only first order effect of PMD but also that of all-ordereffect of PMD.

PMD can be characterized by the PMD vector {right arrow over (τ)}(ω),which may be expanded into a Taylor series about the signal's centerfrequency (see, for example, reference 3). The first term of theexpansion, known as first order PMD, is the differential group delay(DGD) between the two principal states of polarization (PSPs). Sincethis delay is considered to be the dominant mechanism for PMD inducedsystem impairment, the penalty has been related to the power in each ofthe PSPs and the DGD (see, for example, reference 3). However, thismodel does not consider the effects of higher-order PMD.

The inventors have realized that the first-order PMD-induced systempenalty can be represented by a measurable channel characteristic, astate of polarization (SOP) ‘string’, which is the length of a curve onthe Poincare sphere traced by the output SOP as the frequency sweepsacross the modulation bandwidth (see, for example, reference 4). Using afirst order approximation for this model, the PMD-induced power penaltyarising from purely first order PMD sources was compared with that froma fiber with all orders of PMD present. It was found that adeterministic correction should be made to the first-order PMD-inducedpenalty approximation for both first and all-order PMD. Further, it wasshown that higher orders of PMD introduce an additional scatter that iscorrelated with the magnitude of the second order PMD vector and nearlyindependent of the length of the SOP string.

To characterize the relationship between PMD and system performance, theOSNR penalties were measured for three different PMD sources. Two werefirst-order PMD sources comprising polarization maintaining (PM) fiberswith DGDs of 26 ps and 60 ps, and lengths of 100 m and 60 m,respectively. The third was an all-order PMD source comprising 12 km ofmechanically and thermally stabilized high PMD fiber compensated forchromatic dispersion. Its DGD had a mean of 30.8 ps, and ranged between10.9 ps and 52.5 ps over the frequencies of interest.

The system penalty was characterized by measuring the change in OSNR,relative to a back-to-back measurement, required to maintain a constantBER of 10⁻⁹. The experimental setup shown in FIG. 1 uses a tunable laser114 with an integrated zero-chirp 15 dB extinction ratio modulator togenerate a single optical channel transmitting a 2²³−1non-return-to-zero (NRZ) pseudo-random bit sequence (PRBS generatorelement 112) at 10 Gb/s.

The optical eye for a back-to-back measurement is shown in the inset ofFIG. 2. The OSNR was controlled by combining the signal in a 90:10coupler 125 (FIG. 1) with a depolarized amplified spontaneous emission(ASE) noise source. The noise was generated by a first erbium-dopedfiber amplifier (EDFA) 102 with open input to generate amplifiedspontaneous emission, essentially an optical version of white noise.First EDFA 102 is followed by a tunable 1.2 nm grating filter 104centered on the signal wavelength, followed by a second EDFA 106. ASEloading was controlled with an optical attenuator 108 positioned betweenEDFA 106 and coupler 125.

At one output of coupler 125, the input SOP was set using a polarizationcontroller 130 before launching both the signal and ASE noise into thePMD source 135. This fixes the signal polarization relative to anyresidual polarization of ASE noise, resulting from the weak polarizationdependence of the grating filter. The other output of coupler 125 wasconnected to an optical spectrum analyzer (OSA) used for OSNRmeasurements.

At the output of the PMD source 135, the signal is passed into a 3 dBcoupler 140. One coupler output was connected to a monitoringpolarimeter 142. The other coupler output was passed through anattenuator 152, EDFA, 154, filter 156, attenuator 158, to an opticallypre-amplified OC-192 receiver 160. Receiver 160 has a 0.25 nm opticalfilter, and is connected to a bit error rate (BER) tester. Results werecollected from forty-one frequency channels at 50 GHz spacing on the ITUgrid between 193.0 to 195.0 THz.

For each channel, PMD measurements were initially taken across a 40 GHzfrequency band centered at the channel's optical frequency, using thetunable probe laser, polarization controller and polarimeter. The DGDand PSP for each channel were determined from this data using theMüiller Matrix Method (see, for example, reference 5). Data was thentransmitted over the channel using the modulated tunable laser. The datasignal's launch SOP was rotated through 20 pre-programmed states thatgave uniform coverage of the Poincaré sphere.

For each launch SOP, the ASE loading was adjusted in 1 dB steps toproduce OSNRs of between 15 and 25 dB; the decision timing and thresholdof the BER decision circuit were optimized; and the BER and OSNR wererecorded. Finally, the PMD measurement across the same 40 GHz bandwidthwas repeated to estimate the stability of the channel's PMD vectorthroughout the duration of the measurements, before moving to the nextchannel. Since the same polarimeter was used to measure the PSP of thePMD source and the signal's SOP, it is possible to calculate the anglebetween these two measured vectors. The back-to-back OSNR for eachchannel varied between 20.1 and 20.6 dB, with the variation attributedto the polarization dependence of the OSA and optical filters.

The PMD-induced OSNR penalty is often approximated to the first order bythe following empirical expression (see, for example, reference 3):

$\begin{matrix}{{ɛ\left( \overset{\rightharpoonup}{\tau} \right)} = {A_{0}{\gamma\left( {1 - \gamma} \right)}\left( \frac{\tau}{T} \right)^{2}}} & (1)\end{matrix}$

in which:

-   -   ε is the PMD-induced OSNR penalty;    -   {right arrow over (τ)} is the PMD vector at the input;    -   A₀ is a modulation-format-specific constant;    -   γ is the splitting ratio between the two PSPs;    -   τ is differential group delay (DGD); and    -   T is the bit period.

Eq. 1 can be rewritten in terms of the length of an SOP trace on thePoincaré sphere as the frequency moves across the modulation bandwidth1/T. This ‘string’ is a measurable quantity, which represents thedepolarization of a signal, and can be separated from other impairmentsaffecting the signal performance (see, for example, references 4, 6, 7).The first order approximation for this string length is given by:L ₁=(τ/T)sin θ

in which θ is the angle between the PSP and the launch SOP. With thisnotation, Eq. (1) can be rewritten to show that the penalty ε is relatedto the string length L₁ through a quadratic relationship:

$\begin{matrix}{ɛ = {\frac{A_{0}}{4}L_{1}^{2}}} & (2)\end{matrix}$

Since string length L₁ can be determined either directly from spectrallyresolved polarimetry, or by measuring θ and τ, the applicability of Eq.2 to pure first order and to higher order PMD may be investigated byplotting the OSNR penalties at BER=10⁻⁹ against the corresponding stringlength approximation L₁. FIG. 2 compares the results for the two firstorder PMD fibers, with DGDs of 26 ps and 60 ps. The coefficient in Eq. 2was extracted from the lower bound of the 26 ps data and found A₀=49.6,which is remarkably close to the A₀=48.3 reported in reference 2 for NRZmodulation. The corresponding penalty from Eq. (2) is shown as a dashedline. While the fit is good at small string lengths, the 60 ps resultsat higher string lengths show a strong deviation. Instead, this data iswell fitted by the quartic polynomial:ε=AL ₁ ²/4+BL ₁ ⁴  (3)

The quartic polynomial includes a higher order term, and is similar tothat in other publications (see, for example, reference 2). In our case,the best fit for the lower bound is obtained with A=40 and B=36. WhileEq. 3 is not the only form a correction to the first order penaltyapproximation could take, it is a convenient choice as it lends itselfto analytical analysis of PMD outages (see, for example, reference 8).For example, if the DGD follows a Maxwellian distribution then thesystem outage probability (that is, the probability of the penalty toexceed ε_(out) dB) becomes:P _(out)=exp(ν−ν√{square root over (1+ε_(out)/η))}  (4)

in which:

-   -   P_(out) is the system outage penalty;    -   ν=3A/(16Br²);    -   r=τ_(rms)T is the ratio between the rms DGD and the bit period;    -   η=A²/(64B); and    -   ε_(out) is the maximum optical signal-to-noise ratio (OSNR)        penalty a system can tolerate before going into outage.

The applicability of Eq. (3) to the all-order PMD fiber data is shown inFIG. 3. It is clear that (i) the quartic fit for the first-order dataserves as a lower bound for the all-order data, and (ii) the penaltyscatter is considerably higher for the all-order data, exceeding theexperimental error of 0.5 dB in OSNR measurement.

To evaluate the data further, the OSNR penalty data was sorted into SOPstring length bins of width 0.02. FIG. 4 shows the mean and range ofpenalty values in each bin. The figure reveals another interestingfeature of the data: the penalty scatter is approximately constant forthe all-order PMD data, but appears to increase with string length forthe first order data, particularly for higher values. To find the cause,a comparison was made of the stability of the three fibers using the rmsdrift of the received SOP over the measurement time for each launch SOPand channel investigated. The inset of FIG. 4 compares the distributionof these drifts for the three fibers and shows that the 60 ps highbirefringence fiber has greater SOP drift, which accounts for theincreased spread of the first order data at higher string lengths.

Since the approximation for string length used here, neglects the effecthigh-order PMD, the additional spread of the all-order data wasattributed to higher orders of PMD. To study this, FIG. 5 plots thepenalty spread of the all-order PMD data from each channel against themagnitude of its second order PMD vector. The figure shows that thepenalty spread increases with the magnitude of the second order PMD. Alinear fit gives a correlation coefficient of R²=0.77. However, theexperimental results indicate that Eq. 3 adequately describes therelationship between the system penalty and string length despite thisadditional scatter.

It may be concluded that the empirical quadratic approximation forPMD-induced OSNR penalty holds for a purely first order PMD source withsmall DGDs. However, larger DGDs, and the presence of high-order PMDincreases the penalty, which follows a quartic dependence on ‘string’length. The first order data acts as a lower bound for the all-orderdata, whose additional scatter is attributed to higher orders of PMD.The amount of higher-order penalty scatter is nearly independent of the‘string’ length, and can be correlated with the magnitude of the secondorder PMD vector. Further, the string approach is shown to be a goodpredictor of the OSNR penalty.

FIG. 6 is a flowchart of one practical embodiment of a method ofdetermining the polarization mode dispersion (PMD) induced systempenalty ε of an optical transmission system. The illustrated methodinvolves a first portion in which the system penalty is calculated, anda second portion in which the calculated system penalty is used in someuseful application.

One embodiment is based on the calculation of the system penalty basedgenerally on Eq. 3, above, which may be simplified as:ε=AL ² +BL ⁴  (5)

in which:

-   -   A and B are predetermined parameters that may be constants, and    -   L is an SOP string length.

Referring again to FIG. 6, block 600 indicates the calculation ofparameters A and B for a particular system. In one embodiment, A and Bare constants. A and B depend on the designs of the transmitter andreceiver, and may be calculated in advance by fitting the measuredpenalty against string length data with Eq. 5.

Block 605 indicates beginning of transmission on the optical fiber inquestion,

Block 610 indicates the tapping of an optical wavelength divisionmultiplexed (WDM) signal from the fiber. In one embodiment, this tappingis performed by an optical coupler.

Block 615 indicates the separating of an optical channel of interestfrom the optical WDM signal that was tapped in block 610. In oneembodiment, this separating step is performed using an optical bandpassfilter.

It is readily appreciated by those skilled in the art that the order ofblocks 610 and 615, like others described in this disclosure, may bereversed.

Block 620 indicates the measurement of string length L. String length isobtained from a frequency-resolved state of polarization (SOP)measurement by calculating the length of a state of polarization trace.In one implementation, this length is spectrally weighted. Frequencyresolved SOP measurement may be performed by optically resolvedpolarimetry (see, for example, reference 7). Alternatively, stringmeasurement may be performed using heterodyne polarimetry (see, forexample, reference 4, and co-pending U.S. application Ser. No.10/825,529, filed Apr. 15, 2004, entitled Method and Apparatus forMeasuring Frequency-Resolved States of Polarization of a Working OpticalChannel Using Polarization-Scrambled Heterodyning, which is incorporatedherein by reference).

Those skilled in the art may perform string measurement without undueexperimentation (see, for example, references 4, 6, 7). In oneembodiment, string measurement is computed according to a formula:

$\begin{matrix}{L = \frac{\int{{I(\omega)}{{{\mathbb{d}S}/{\mathbb{d}\omega}}}{\mathbb{d}\omega}}}{T{\int{{I(\omega)}{\mathbb{d}\omega}}}}} & (6)\end{matrix}$

in which:

-   -   I(ω) is a weighting function such as an optical spectrum density        function;    -   ω is frequency;    -   S(ω) is the frequency-resolved state of polarization (SOP); and    -   T is a bit period.

Given a value of L, block 625 indicates computation of the polarizationmode dispersion (PMD) induced system penalty ε. In one embodiment, ε iscomputed according to Eq. 5, above, and as shown in block 600.

As an enhancement, to include the effect of higher orders, anotherstring length parameter may be used that is more generally defined as a“functional” (a function of a function) F[ ]:L=F[{right arrow over (S)}(ω)]  (7)

In Eq. 7, F[ ] is a functional (here a scalar function of a vectorfunction) that minimizes the scatter in FIG. 4 (a graph of PMD-inducedsystem penalty as a function of SOP string length L₁). In oneimplementation, this functional is chosen to include not only the stringlength but also the string curvature as:

$\begin{matrix}{L = {\frac{\int{{I(\omega)}{{{\mathbb{d}S}/{\mathbb{d}\omega}}}{\mathbb{d}\omega}}}{T{\int{{I(\omega)}{\mathbb{d}\omega}}}} + {\alpha\frac{\int{{I(\omega)}{{{\mathbb{d}^{2}S}/{\mathbb{d}\omega^{2}}}}{\mathbb{d}\omega}}}{T^{2}{\int{{I(\omega)}{\mathbb{d}\omega}}}}}}} & (8)\end{matrix}$

in which α is a constant depending on the modulation format and designof the transmitter and receiver.

The PMD-induced system penalty ε, once calculated, may be used in avariety of ways. The manner in which ε is used, depends on theparticular application. Block 650 indicates a choice of application ofthe calculated ε:

-   -   Block 651 indicates a first application of ε, which is to        monitor performance of the optical network of which the optical        fiber in question is a part.    -   Block 652 indicates a second application of ε, which is to        manage the network of which the optical fiber in question is a        part.    -   Block 653 indicates a third application of ε, which is to        actually feed back the value of ε to a compensator element in        order to affirmatively compensate for or mitigate the        degradation that PMD has caused. Given the calculated value of        ε, this compensation or mitigation may be readily implemented by        those skilled in the art.

Of course, the illustrated applications 651, 652, 653 are examples anddo not limit the scope of application of the invention.

After the system penalty is calculated and any application of thecalculated penalty has been carried out, control may return to any of avariety of blocks in FIG. 6. For example, control may return to block600 for a re-calculation of A and B for the same or a different system.Alternatively, control may return to block 605 to begin transmission ofnew or different data, to block 610 to tap the same or a differentoptical SDM signal, to block 615 to separate the same or a differentchannel of interest, or to block 620 to measure string length L again.

The calculations involved in computing the PMD-induced system penaltyand in other monitoring and control steps, may be performed by asuitable general purpose computer or processor arrangement.

In one embodiment, the apparatus is a computer or a cluster ofcomputers, powered by software to execute the functionality describedherein. The functional elements described above may be embodied by anysuitable systems for performing the described methods, the systemsincluding at least one data processing element. Generally, these dataprocessing elements may be implemented as any appropriate computer(s)employing technology known by those skilled in the art to be appropriateto the functions performed. The computer(s) may be implemented using aconventional general purpose computer programmed according to theforegoing teachings, as will be apparent to those skilled in thecomputer art. Appropriate software can readily be prepared byprogrammers based on the teachings of the present disclosure. Suitableprogramming languages operating with available operating systems may bechosen.

General purpose computers may implement the foregoing methods, in whichthe computer housing may house a CPU (central processing unit), memorysuch as DRAM (dynamic random access memory), ROM (read only memory),EPROM (erasable programmable read only memory), EEPROM (electricallyerasable programmable read only memory), SRAM (static random accessmemory), SDRAM (synchronous dynamic random access memory), and Flash RAM(random access memory), and other special purpose logic devices such asASICs (application specific integrated circuits) or configurable logicdevices such GAL (generic array logic) and reprogrammable FPGAs (fieldprogrammable gate arrays).

Each computer may also include plural input devices (for example,keyboard, microphone, and mouse), and a display controller forcontrolling a monitor. Additionally, the computer may include a floppydisk drive; other removable media devices (for example, compact disc,tape, and removable magneto optical media); and a hard disk or otherfixed high-density media drives, connected using an appropriate devicebus such as a SCSI (small computer system interface) bus, an EnhancedIDE (integrated drive electronics) bus, or an Ultra DMA (direct memoryaccess) bus. The computer may also include a compact disc reader, acompact disc reader/writer unit, or a compact disc jukebox, which may beconnected to the same device bus or to another device bus.

The invention envisions at least one computer readable medium. Examplesof computer readable media include compact discs, hard disks, floppydisks, tape, magneto optical disks, PROMs (for example, EPROM, EEPROM,Flash EPROM), DRAM, SRAM, SDRAM. Stored on any one or on a combinationof computer readable media is software for controlling both the hardwareof the computer and for enabling the computer to interact with otherelements, to perform the functions described above. Such software mayinclude, but is not limited to, user applications, device drivers,operating systems, development tools, and so forth. Such computerreadable media further include a computer program product includingcomputer executable code or computer executable instructions that, whenexecuted, causes a computer to perform the methods disclosed above. Thecomputer code may be any interpreted or executable code, including butnot limited to scripts, interpreters, dynamic link libraries, Javaclasses, complete executable programs, and the like.

From the foregoing, it will be apparent to those skilled in the art thata variety of methods, systems, computer programs on recording media, andthe like, are provided.

The present disclosure supports a method for determining a polarizationmode dispersion (PMD) induced system penalty ε from the opticalcharacteristics of an optical wavelength division multiplexed (WDM)signal carried on a network. The method involves tapping the optical WDMsignal, separating an optical channel from the tapped optical WDMsignal, performing a frequency-resolved state of polarization (SOP)measurement on the channel, and computing the PMD-induced system penaltyas ε=AL²+BL⁴ in which A and B are predetermined parameters and L is anSOP string length based on the SOP measurement.

The step of performing a frequency-resolved SOP measurement may includeperforming a string length measurement by a frequency-resolved SOPoptical-domain measurement.

The string length measurement may include performing the string lengthmeasurement using heterodyne polarimetry.

The method may also involve demultiplexing the optical WDM signal beforethe signal tapping step.

The method may also involve performing monitoring and network managementusing the computed PMD-induced system penalty ε.

The method may also involve compensating for or mitigating thepolarization mode dispersion by feeding the computed PMD induced systempenalty ε back to a PMD compensation arrangement.

L may be a weighted string length expressed as:

$L = \frac{\int{{I(\omega)}{{{\mathbb{d}S}/{\mathbb{d}\omega}}}{\mathbb{d}\omega}}}{T{\int{{I(\omega)}{\mathbb{d}\omega}}}}$

in which I(ω) is a weighting function, ω is frequency, S(ω) is frequencyresolved state of polarization, and T is a bit period.

The weighting function I(ω) may be an optical spectrum of the signal.

The tapping, separating, performing and computing steps may be carriedout without interrupting operation of the network.

The optical channel separating step may include separating the opticalchannel using an optical bandpass filter.

The signal tapping step may include tapping the optical WDM signal usingan optical coupler.

A and B may be predetermined constants.

The string length L may include a functional F[ ]:L=F[{right arrow over (S)}(ω)]

wherein functional F[·] is a scalar function of a vector function, andis configured to minimize scatter in a graph of PMD-induced systempenalty as a function of SOP string length.

The functional F[ ] may include string curvature so that:

$L = {\frac{\int{{I(\omega)}{{{\mathbb{d}S}/{\mathbb{d}\omega}}}{\mathbb{d}\omega}}}{T{\int{{I(\omega)}{\mathbb{d}\omega}}}} + {\alpha\frac{\int{{I(\omega)}{{{\mathbb{d}^{2}S}/{\mathbb{d}\omega^{2}}}}{\mathbb{d}\omega}}}{T^{2}{\int{{I(\omega)}{\mathbb{d}\omega}}}}}}$

in which α is a constant.

The present disclosure also supports a computer program productincluding computer executable code or computer executable instructionsthat, when executed, causes at least one computer to execute theperforming and computing steps described herein.

The present disclosure also supports a system configured to execute theperforming and computing steps described herein.

Many alternatives, modifications, and variations will be apparent tothose skilled in the art in light of the above teachings. Of course,those skilled in the art readily recognize that there are numerousapplications of the invention beyond those described herein. While thepresent invention has been described with reference to one or moreparticular embodiments, those skilled in the art recognize that manychanges may be made thereto without departing from the spirit and scopeof the present invention. It is therefore to be understood that withinthe scope of the appended claims and their equivalents, the inventionmay be practiced otherwise than as specifically described herein.

1. A method for determining a polarization mode dispersion (PMD) inducedsystem penalty ε from the optical characteristics of an opticalwavelength division multiplexed (WDM) signal carried on a network, themethod comprising: tapping the optical WDM signal; separating an opticalchannel signal from the tapped optical WDM signal; performing afrequency-resolved state of polarization (SOP) measurement on thechannel; computing the PMD-induced system penalty as ε=AL²+BL⁴; wherein:A and B are predetermined parameters; and L is an SOP string lengthbased on the SOP measurement; and outputting the PMD-induced systempenalty ε to an application.
 2. The method of claim 1, wherein the stepof performing a frequency-resolved SOP measurement includes: performinga string length measurement by a frequency-resolved SOP optical-domainmeasurement.
 3. The method of claim 2, wherein the string lengthmeasurement includes: performing the string length measurement usingheterodyne polarimetry.
 4. The method of claim 1, further comprising:demultiplexing the optical WDM signal before the signal tapping step. 5.The method of claim 1, further comprising: performing monitoring andnetwork management using the computed PMD-induced system penalty ε. 6.The method of claim 1, further comprising: compensating for ormitigating the polarization mode dispersion by feeding the computedPMD-induced system penalty ε back to a PMD compensation arrangement. 7.The method of claim 1, wherein L is a weighted string length expressedas:$L = \frac{\int{{I(\omega)}{{{\mathbb{d}S}/{\mathbb{d}\omega}}}{\mathbb{d}\omega}}}{T{\int{{I(\omega)}{\mathbb{d}\omega}}}}$wherein: I(ω) is a weighting function; ω is frequency; S(ω) is frequencyresolved state of polarization; and T is a bit period.
 8. The method ofclaim 7, wherein: the weighting function I(ω) is an optical spectrum ofthe signal.
 9. The method of claim 1, wherein: the tapping, separating,performing and computing steps are carried out without interruptingoperation of the network.
 10. The method of claim 1, wherein the opticalchannel separating step includes: separating the optical channel usingan optical bandpass filter.
 11. The method of claim 1, wherein thesignal tapping step includes: tapping the optical WDM signal using anoptical coupler.
 12. The method of claim 1, wherein: A and B arepredetermined constants.
 13. The method of claim 1, wherein the stringlength L includes a functional F[ ]:L=F[ S (ω)] wherein functional F[ ] is a scalar function of a vectorfunction, and is configured to minimize scatter in a graph ofPMD-induced system penalty as a function of SOP string length.
 14. Themethod of claim 13, wherein the functional F[ ] includes stringcurvature so that:$L = {\frac{\int{{I(\omega)}{{{\mathbb{d}S}/{\mathbb{d}\omega}}}{\mathbb{d}\omega}}}{T{\int{{I(\omega)}{\mathbb{d}\omega}}}} + {\alpha\frac{\int{{I(\omega)}{{{\mathbb{d}^{2}S}/{\mathbb{d}\omega^{2}}}}{\mathbb{d}\omega}}}{T^{2}{\int{{I(\omega)}{\mathbb{d}\omega}}}}}}$wherein α is a constant.
 15. A computer-usable medium having computerreadable instructions stored thereon for execution by a processor toperform a method for determining a polarization mode dispersion (PMD)induced system penalty ε from the optical characteristics of an opticalwavelength division multiplexed (WDM) signal carried on a network, themethod comprising: tapping the optical WDM signal; separating an opticalchannel signal from the tapped optical WDM signal; performing afrequency-resolved state of polarization (SOP) measurement on thechannel; computing the PMD-induced system penalty as ε=AL²+BL⁴; wherein:A and B are predetermined parameters; and L is an SOP string lengthbased on the SOP measurement; and outputting the PMD-induced systempenalty ε to an application.
 16. The computer-usable medium of claim 15,wherein the step of performing a frequency-resolved SOP measurementincludes: performing a string length measurement by a frequency-resolvedSOP optical-domain measurement.
 17. The computer-usable medium of claim16, wherein the string length measurement includes: performing thestring length measurement using heterodyne polarimetry.
 18. Thecomputer-usable medium of claim 15, wherein L is a weighted stringlength expressed as:$L = \frac{\int{{I(\omega)}{{{\mathbb{d}S}/{\mathbb{d}\omega}}}{\mathbb{d}\omega}}}{T{\int{{I(\omega)}{\mathbb{d}\omega}}}}$wherein: I(ω) is a weighting function; ω is frequency; S(ω) is frequencyresolved state of polarization; and T is a bit period.
 19. Thecomputer-usable medium of claim 15, wherein the string length L includesa functional F[ ]:L=F[ S (ω)] wherein functional F[ ] is a scalar function of a vectorfunction, and is configured to minimize scatter in a graph ofPMD-induced system penalty as a function of SOP string length.
 20. Asystem for determining whether network errors are due to polarizationmode dispersion (PMD) using a PMD induced system penalty εdeterminedfrom the optical characteristics of an optical wavelength divisionmultiplexed (WDM) signal carried on a network, the system comprising: anoptical WDM signal tap; means for separating an optical channel signalfrom the tapped optical WDM signal; means for performing afrequency-resolved state of polarization (SOP) measurement on thechannel; means for computing the PMD-induced system penalty asε=AL²+BL⁴; wherein: A and B are predetermined parameters; and L is anSOP string length based on the SOP measurement; and wherein thePMD-induced system penalty ε is used for determining whether networkerrors are due to PMD.